\ String theory for Nuclear physics Sang-Jin Sin (Hanyang meeting

Why string theory? I. Since there is a string in QCD Confinement  Flux string or QCD string That is how string theory began 40 years ago. But not the reason today.

Why string theory? II Shear viscosity /entropy density in RHIC experiment: < 0.1 pQCD: String Theory : ~ 1/4 π =0.09 The method used is AdS/CFT Q: Confinement and Hadron physics?

Gauge/gravity duality (ads/cft) Maldacena, GKP, Witten, D brane can be described in 2 ways. One is gauge theory The other is string theory in curved spacetime. So they must be equivalent. In certain limit, the latter is Einstein gravity theory

Character of AdS/CFT 1. Holographic: 5d gravity theory for 4d QCD origin of +1 dim? Scale z direction is warped!  ads Stolen from Hong Liu

Character of AdS/CFT II Within the validity, Do not need loop calculation. 1. ls<<Rads 2. gs<<1 Large N theory. Good and Bad

Character of AdS/CFT III Super-symmetry Original version is N=4 SUSY. SUSY can be broken by BC. T. d. etc Is it QCD? Hopefully some properties will be univer sal. Some results are too good to be irrel evant …… [eta/s, glueon mass, ads/qcd, SS]

Ads/cft Dictionary Let O(x) is an color singlet operator with dimension and spin p A(x) is an source of it. Then AdS/CFT says: Extend it to d+1(=5) dim by If we know action and BC, it can be calculated CLASSICALLY. So is all correlation functions and its corollaries.

Density and chemical potential In 4d, Source of baryon number op is Extend it to 5dim by

Gluon condensation and dilaton Tr(F^2) is dual to scalar Extend it to 5dim by

Chiral condensation and mass Mass op. is dual to a scalar Extend it to 5 dim by

Temperature

Gluon dynamics  Geometry. Confinement or deConfinement depends on geometry.

Goemetry with

Geometry with Zm

What can one do with it. Phase transition, equation of state. Two point function  Transports. Spectral fct Viscosity conductivity heat cd Elliptic flow(time dependence) Dissipation and energy loss. (dragging) Meson/Baryon spectrum Symmetry energy Lepto and Photo emission rate …………..…….

Bottom up model Write down linear sigma model in ads5. with chiral symmetry SU(Nf)xSU(Nf) Roughly, X=sU, by hand. No Potential No loop calcalculation: Point of the theory: Throw away Kaluza Klein

Observables Interaction: Overlapping integral Decay constant: GOR relation Mass spectrum:

Resuls: too good to be true?

Top down Quark: Bifundamental, Meson: adjoint Dynamics: Dirac-Born-Infeld action Baryon: compact D5 D3 D7

Baryon density and meson at probe D7

BR-scaling In 1991, G.Brown and M.Rho Q: Is it true?

D4/D6 model Confining geometry.

Result: Yes in a model. Embedding: Vector Mass GOR relation is true in Medium.

Symmetry energy I Def: Present status:

Symmetry energy II Main idea: different isospin ~ different number of strings attached to tw o probe brane

Symmetry energy : result Stiff  neutron star crest is Thin.

Pauli principle in hQCD. two puzzles in 4d: Driving force of Z=N is Pauli principle. Ads/cft is count ing QM by classical dynamics. So how to count Pauli force. In 5d: coulomb force by charge. But charge is dual to baryon number, which is global charge. So what is dual of the coulo mb force?

String theory began as a Hadron Th. Confinement  Flux string or QCD string

Conclusion One can do many things Omitted: Elliptic flow. Photo/Lepto emission in LHC? Non-fermiliquid Color superconductivity what I have shown is just tip of iceberg. Not really QCD but may be relevant. Can we do something together?

. QCD string: good for Reggestrajectory bad for deep inelastic scattering data